CONNECTIVITY INDICES OF COPRIME GRAPH OF GENERALIZED QUATERNION GROUP

Abstract

Generalized quaternion group (Q4n) is a group of order 4n that is generated by two elements x and y with the properties x2n = y4 = e and xy = yx−1. The coprime graph of Q4n, denoted by ΩQ4n, is a graph with the vertices are elements of Q4n and the edges are formed by two elements that have coprime order. The first result of this paper presents that ΩQ4n is a tripartite graph for n is an odd prime and ΩQ4n is a star graph for n is a power of 2. The second one presents the connectivity indices of ΩQ4n. Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.